The sum of two numbers is 103. If twice the smaller number is subtracted from the larger number, the result is 16. Find the two numbers.

Question

The sum of two numbers is 103. If twice the smaller number is subtracted from the larger number, the result is 16. Find the two numbers.

Answer 1

Hello Jalynn

 

Let a = the larger # and b = the smaller #.

 

Eq 1) a + b = 103

 

Eq 2) a - 2b = 16  Rearrange this equation to solve for a.

 

        a = 16 + 2b  Substitute this equation into Eq 1), you get

 

16 + 2b + b = 103

 

3b = 103 - 16

 

3b = 87

 

b = 87 / 3 = 29 (smaller #)

 

 

a = 16 + 2b

 

   = 16 + 2(29)

 

   = 16 + 58 = 74 (the larger #)

 

 

To confirm, a + b = 103

 

74 + 29 = 103!